canoncorr

Syntax

Description

[A,B] = canoncorr(X,Y) computes
the sample canonical coefficients for the n-by-d1 and n-by-d2 data
matrices X and Y. X and Y must
have the same number of observations (rows) but can have different
numbers of variables (columns). A and B are d1-by-d and d2-by-d matrices,
where d = min(rank(X),rank(Y)). The jth
columns of A and B contain the
canonical coefficients, i.e., the linear combination of variables
making up the jth canonical variable for X and Y,
respectively. Columns of A and B are
scaled to make the covariance matrices of the canonical variables
the identity matrix (see U and V below).
If X or Y is less than full
rank, canoncorr gives a warning and returns zeros
in the rows of A or B corresponding
to dependent columns of X or Y.

[A,B,r] = canoncorr(X,Y) also
returns a 1-by-d vector containing the sample canonical
correlations. The jth element of r is
the correlation between the jth columns of U and V (see
below).

[A,B,r,U,V,stats] = canoncorr(X,Y)
also returns a structure stats containing information
relating to the sequence of d null hypotheses H0(k), that the (k+1)st
through dth correlations are all zero, for k
= 0:(d-1). stats contains seven fields,
each a 1-by-d vector with elements
corresponding to the values of k, as described
in the following table:

Field

Description

Wilks

Wilks' lambda (likelihood ratio) statistic

df1

Degrees of freedom for the chi-squared statistic, and
the numerator degrees of freedom for the F statistic